...the difference of the opposite intercepted arcs. PROPOSITION XVII. THEOREM. The opposite angles of a quadrilateral inscribed in a circle, are together equal to two right angles. The opposite angles A, C, or ABC, ADC, of the inscribed quadrilateral ABCD, are together equal to two...

...externally, the straight line which joins their centres, shall pass through the point of contact. 10. The opposite angles of any quadrilateral inscribed...a circle, are together equal to two right angles. 11. If a straight line touch a circle, and from the point of contact a straight line be drawn cutting...

...the difference of the angles BDE, ADE, will be invariable. SECTION III. 1. The opposite angles of Buy quadrilateral inscribed in a circle, are together equal to two right angles. No parallelogram can be inscribed in a circle, unless it be rectangular. 2. In equal circles the angles...

...part. Deduce the same from the preceding propositions of the Second Book. 6. The opposite angles of a quadrilateral inscribed in a circle, are together equal to two .right angles. Shew that no parallelogram, except a rectangle, can be inscribed in a circle. 7. If a straight line...

...equal to the square of the line made up of the half and the produced part. 3. The opposite angles of a quadrilateral inscribed in a circle are together equal to two right angles. o. If the opposite angles of a quadrilateral are together equal to two right angles, the quadrilateral...

...[-*]"" = (~1)a ; also, [-*]» - 1. * 1531 (Proposed by Dr. BOOTH, FRS)— " The opposite angles of a quadrilateral inscribed in a circle are together equal to two right angles." What is the more general theorem in the conic sections, of which this is a particular case P Solution...

...expression 2 sin £(o + 0) sin £(0 + 7) sin 4(7 + a). ............ 79 1531. " The opposite angles of a quadrilateral inscribed in a circle are together equal to two right angles." What is the more general theorem in the conic sections, of which this is a particular case ? 1532....

...E and F, join EF, prove EF perpendicular to AD. 10. The opposite angles of any quadrilateral figure inscribed in a circle are together equal to two right angles. Show that the sum of the angles contained in the four segments of the circle external to the quadrilateral is...

...shew that at least one of its angles must be greater than a right angle. III. The opposite angles of a quadrilateral inscribed in a circle are together equal to two right angles. IV. The rectangle contained by the diagonals of a quadrilateral inscribed in a circle is equal to the...

...diagonals of a parallelogram is equal to the sum of the squares on the sides. 11. The opposite angles of a quadrilateral inscribed in a circle are together equal to two right angles. 12. The straight linns bisecting the Bides of a triangle at right angles meet in a point. 13. Construct...